Page 105 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes
Example 6: solve

dy y 1
dx x 2 1 x 2 1
Let y uv

dx
Here u e 1 x 2 e tan 1 x

1 x dx
tan
so that v e
1 x 2
Let tan x t
1
dx
dt 2
1 x
t
v e dt e t e tan 1 x

Thus y uv

1 x tan 1 x tan 1 x
tan
a e e .e
= 2
a e tan 1 x 1
= 2
Self Assessment

5. Solve by the method (A):

dy
y cosx 0
dx
6. Solve by the method (B):
2 sin ydx x 2 cosydy 0
x
7. Solve by the method (C):

xdy ydx xydx 0
8. Solve by the method (D):

dy 2 2
y x cos3x
dx x
5.4 Summary

 Various differential equations are introduced for their classification.
 Some differential equations are set up after illuminating the constants from the equations
relating x and y.

 Some methods of solving differential equations are given.

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